To solve for g in a = (g + h)/2, algebraic manipulation yields g = 2a - h. Substituting back verifies the solution, showing g is half the sum of a and h.
To isolate g in the equation a = (g + h)/2, we can employ algebraic manipulations. First, we multiply both sides by 2 to eliminate the denominator:
2a = g + h
Next, to isolate g, we subtract h from both sides:
2a - h = g
Therefore, the expression g is given by 2a - h.
In this equation, g represents a value that is half the sum of a and h. If we double-check our result, we can substitute 2a - h back into the original equation:
a = (2a - h + h)/2
By simplifying the right side, we get:
a = (2a)/2
This confirms that the expression 2a - h is indeed a valid solution for g.